VRBO.com. Vacation Rental by Owner. Flats, apartments, condos etc ...
Same as hotels, central London will be more expensive given the location but move a bit further out, South Kensington, Earls Court etc and you can find better deals.
Edit: Totally guessed on dates but here is a quick search in London...
https://www.vrbo.com/search/keywords...&adultsCount=2